with \(\rho _{i}\)  being the eigenvalue of the reduced density matrix \(\hat{\rho }_{l}=\mathrm {Tr}_{L-l}|\psi \rangle \langle \psi |\) , where \(|\psi \rangle \)  is the ground-state wave-function of Hamiltonian (REF ) and \(l\)  is the length of the left block for a specific bipartition. The quantum criticality of the
interaction-driven topological phase transition can be characterized with the von
Neumann entropy [1]}, [2]}, [3]}, [4]}, [5]}, [6]}
\(S_{\mathrm {vN}}=-\mathrm {Tr}_{l}[\hat{\rho }_{l}\log \hat{\rho }_{l}],\) 
